Abstract and Applied Analysis

Common Fixed Points for Weak ψ-Contractive Mappings in Ordered Metric Spaces with Applications

Sumit Chandok and Simona Dinu

Full-text: Open access

Abstract

We obtain some new common fixed point theorems satisfying a weak contractive condition in the framework of partially ordered metric spaces. The main result generalizes and extends some known results given by some authors in the literature.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 879084, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393443518

Digital Object Identifier
doi:10.1155/2013/879084

Mathematical Reviews number (MathSciNet)
MR3108631

Zentralblatt MATH identifier
1303.54015

Citation

Chandok, Sumit; Dinu, Simona. Common Fixed Points for Weak ψ -Contractive Mappings in Ordered Metric Spaces with Applications. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 879084, 7 pages. doi:10.1155/2013/879084. https://projecteuclid.org/euclid.aaa/1393443518


Export citation

References

  • M. Abbas, Y. J. Cho, and T. Nazir, “Common fixed point theorems for four mappings in TVS-valued cone metric spaces,” Journal of Mathematical Inequalities, vol. 5, no. 2, pp. 287–299, 2011.
  • M. Abbas and M. A. Khan, “Common fixed point theorem of two mappings satisfying a generalized weak contractive condition,” International Journal of Mathematics and Mathematical Sciences, vol. 2009, Article ID 131068, 9 pages, 2009.
  • M. Abbas, T. Nazir, and S. Radenović, “Common fixed points of four maps in partially ordered metric spaces,” Applied Mathematics Letters, vol. 24, no. 9, pp. 1520–1526, 2011.
  • I. Altun, B. Damjanović, and D. Djorić, “Fixed point and common fixed point theorems on ordered cone metric spaces,” Applied Mathematics Letters, vol. 23, no. 3, pp. 310–316, 2010.
  • H. Aydi, M. Postolache, and W. Shatanawi, “Coupled fixed point results for $(\psi ,\phi )$-metric spaces,” Computers & Mathematics with Applications, vol. 63, no. 1, pp. 298–309, 2012.
  • H. Aydi, E. Karapinar, and M. Postolache, “Tripled coincidence point theorems for weak $\phi $-contractions in partially ordered metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 44, 2012.
  • H. Aydi, W. Shatanawi, M. Postolache, Z. Mustafa, and N. Tahat, “Theorems for Boyd-Wong-type contractions in ordered metric spaces,” Abstract and Applied Analysis, vol. 2012, Article ID 359054, 14 pages, 2012.
  • T. Gnana Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications,” Nonlinear Analysis. Theory, Methods & Applications, vol. 65, no. 7, pp. 1379–1393, 2006.
  • A. Branciari, “A fixed point theorem for mappings satisfying a general contractive condition of integral type,” International Journal of Mathematics and Mathematical Sciences, vol. 29, no. 9, pp. 531–536, 2002.
  • S. Chandok, “Some common fixed point theorems for generalized $f$-weakly contractive mappings,” Journal of Applied Mathematics & Informatics, vol. 29, no. 1-2, pp. 257–265, 2011.
  • S. Chandok, “Some common fixed point theorems for generalized nonlinear contractive mappings,” Computers & Mathematics with Applications, vol. 62, no. 10, pp. 3692–3699, 2011.
  • S. Chandok, “Common fixed points, invariant approximation and generalized weak contractions,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 102980, 11 pages, 2012.
  • S. Chandok, “Some common fixed point results for generalized weak contractive mappings in partially ordered metric spaces,” Journal of Nonlinear Analysis and Optimization, vol. 4, no. 1, pp. 45–52, 2013.
  • S. Chandok, M. S. Khan, and K. P. R. Rao, “Some coupled common fixed point theorems for a pair of mappings satisfying a contractive condition of rational type without monotonicity,” International Journal of Mathematical Analysis, vol. 7, no. 9-12, pp. 433–440, 2013.
  • S. Chandok, Z. Mustafa, and M. Postolache, “Coupled common fixed point theorems for mixed g-monotone mappings in partially ordered G-metric spaces,” UPB Scientific Bulletin A. In press.
  • S. Chandok and M. Postolache, “Fixed point theorem for weakly Chatterjea-type cyclic contractions,” Fixed Point Theory and Applications, vol. 2012, article 28, 2013.
  • S. Chandok, W. Sintunavarat, and P. Kumam, “Some coupled common fixed points for a pair of mappings in partially ordered G-metric spaces,” Mathematical Sciences, vol. 7, article 24, 2013.
  • C.-M. Chen, “Fixed point theorems for $\psi $-contractive mappings in ordered metric spaces,” Journal of Applied Mathematics, vol. 2012, Article ID 756453, 10 pages, 2012.
  • B. S. Choudhury, N. Metiya, and M. Postolache, “A generalized weak contraction principle with applications to coupled coincidence point problems,” Fixed Point Theory and Applications, vol. 2013, article 152, 2013.
  • L. Ćirić, “A generalization of Banach's contraction principle,” Proceedings of the American Mathematical Society, vol. 45, no. 2, pp. 26–273, 1974.
  • A. Djoudi and L. Nisse, “Greguš type fixed points for weakly compatible maps,” Bulletin of the Belgian Mathematical Society, vol. 10, no. 3, pp. 369–378, 2003.
  • E. Graily, S. M. Vaezpour, R. Saadati, and Y. J. Cho, “Generalization of fixed point theorems in ordered metric spaces concerning generalized distance,” Fixed Point Theory and Applications, vol. 2011, article 30, 2011.
  • R. H. Haghi, M. Postolache, and Sh. Rezapour, “On T-stability of the Picard iteration for generalized $\varphi $-contraction mappings,” Abstract and Applied Analysis, vol. 2012, Article ID 658971, 7 pages, 2012.
  • G. Jungck, “Compatible mappings and common fixed points,” International Journal of Mathematics and Mathematical Sciences, vol. 9, no. 4, pp. 771–779, 1986.
  • G. Jungck, “Compatible mappings and common fixed points. II,” International Journal of Mathematics and Mathematical Sciences, vol. 11, no. 2, pp. 285–288, 1988.
  • G. Jungck, “Common fixed points for commuting and compatible maps on compacta,” Proceedings of the American Mathematical Society, vol. 103, no. 3, pp. 977–983, 1988.
  • G. Jungck and B. E. Rhoades, “Fixed points for set valued functions without continuity,” Indian Journal of Pure and Applied Mathematics, vol. 29, no. 3, pp. 227–238, 1998.
  • G. Jungck and B. E. Rhoades, “Fixed point theorems for occasionally weakly compatible mappings,” Fixed Point Theory, vol. 7, no. 2, pp. 287–296, 2006.
  • J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,” Order, vol. 22, no. 3, pp. 223–239, 2005.
  • J. J. Nieto and R. Rodríguez-López, “Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations,” Acta Mathematica Sinica, vol. 23, no. 12, pp. 2205–2212, 2007.
  • M. O. Olatinwo and M. Postolache, “Stability results of Jungck-type iterative processes in convex metric spaces,” Applied Mathematics and Computation, vol. 218, no. 12, pp. 6727–6732, 2012.
  • A. C. M. Ran and M. C. B. Reurings, “A fixed point theorem in partially ordered sets and some applications to matrix equations,” Proceedings of the American Mathematical Society, vol. 132, no. 5, pp. 1435–1443, 2004.
  • B. Samet and H. Yazidi, “Fixed point theorems with respect to a contractive condition of integral type,” Rendiconti del Circolo Matematico di Palermo, vol. 60, no. 1-2, pp. 181–190, 2011.
  • S. Sessa, “On a weak commutativity condition of mappings in fixed point considerations,” Publications de l'Institut Mathématique, vol. 32, no. 46, pp. 149–153, 1982.
  • W. Shatanawi and M. Postolache, “Some fixed-point results for a $G$-weak contraction in $G$-metric spaces,” Abstract and Applied Analysis, vol. 2012, Article ID 815870, 19 pages, 2012.
  • W. Shatanawi and M. Postolache, “Common fixed point theorems for dominating and weak annihilator mappings in ordered čommentComment on ref. [36?]: Please update the information of these references[15,36?], if possible.metric spaces,” Fixed Point Theory and Applications. In press.
  • W. Shatanawi and M. Postolache, “Common fixed point results of mappings for nonlinear contractions of cyclic form in ordered metric spaces,” Fixed Point Theory and Applications, vol. 2013, article 60, 2013.
  • W. Shatanawi and M. Postolache, “Coincidence and fixed point results for generalized weak contractions in the sense of Berinde on partial metric spaces,” Fixed Point Theory and Applications, vol. 2013, article 54, 2013.
  • W. Shatanawi and A. Pitea, “Omega-distance and coupled fixed point in G-metric spaces,” Fixed Point Theory and Applications, vol. 2013, article 208, 2013.
  • W. Shatanawi and A. Pitea, “Some coupled fixed point theorems in quasi-partial metric spaces,” Fixed Point Theory and Applications, vol. 2013, article 153, 2013.
  • W. Shatanawi, S. Chauhan, M. Postolache, M. Abbas, and S. Radenović, “Common fixed points for contractive mappings of integral type in G-metric spaces,” Journal of Advanced Mathematical Studies, vol. 6, no. 1, pp. 53–72, 2013.